In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.
This paper has been framed to study the propagation of torsional surface waves in an inhomogeneous layer of finite thickness over an initially stressed inhomogeneous half-space. Rigidity, density and initial stress of the half-space are assumed to have linear variation, and in layers linear variation in rigidity and density are also considered. It has been observed that the inhomogeneity parameter and the initial stress play an important role for the propagation of the torsional surface wave. The method of separation of variables is applied to find the displacement field. The dispersion equation of phase velocity is derived. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed. As a particular case it has been seen that the dispersion equation is in agreement with the classical result of the Love wave when the initial stresses and inhomogeneity parameters are neglected.
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